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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

The greenhouse effect and the 2nd law of thermodynamics

What the science says...

The 2nd law of thermodynamics is consistent with the greenhouse effect which is directly observed.

Climate Myth...

2nd law of thermodynamics contradicts greenhouse theory

"The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier 1824, Tyndall 1861, and Arrhenius 1896, and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist." (Gerhard Gerlich)

Skeptics sometimes claim that the explanation for global warming contradicts the second law of thermodynamics. But does it? To answer that, first, we need to know how global warming works. Then, we need to know what the second law of thermodynamics is, and how it applies to global warming. Global warming, in a nutshell, works like this:

The sun warms the Earth. The Earth and its atmosphere radiate heat away into space. They radiate most of the heat that is received from the sun, so the average temperature of the Earth stays more or less constant. Greenhouse gases trap some of the escaping heat closer to the Earth's surface, making it harder for it to shed that heat, so the Earth warms up in order to radiate the heat more effectively. So the greenhouse gases make the Earth warmer - like a blanket conserving body heat - and voila, you have global warming. See What is Global Warming and the Greenhouse Effect for a more detailed explanation.

The second law of thermodynamics has been stated in many ways. For us, Rudolf Clausius said it best:

"Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature."

So if you put something hot next to something cold, the hot thing won't get hotter, and the cold thing won't get colder. That's so obvious that it hardly needs a scientist to say it, we know this from our daily lives. If you put an ice-cube into your drink, the drink doesn't boil!

The skeptic tells us that, because the air, including the greenhouse gasses, is cooler than the surface of the Earth, it cannot warm the Earth. If it did, they say, that means heat would have to flow from cold to hot, in apparent violation of the second law of thermodynamics.

So have climate scientists made an elementary mistake? Of course not! The skeptic is ignoring the fact that the Earth is being warmed by the sun, which makes all the difference.

To see why, consider that blanket that keeps you warm. If your skin feels cold, wrapping yourself in a blanket can make you warmer. Why? Because your body is generating heat, and that heat is escaping from your body into the environment. When you wrap yourself in a blanket, the loss of heat is reduced, some is retained at the surface of your body, and you warm up. You get warmer because the heat that your body is generating cannot escape as fast as before.

If you put the blanket on a tailors dummy, which does not generate heat, it will have no effect. The dummy will not spontaneously get warmer. That's obvious too!

Is using a blanket an accurate model for global warming by greenhouse gases? Certainly there are differences in how the heat is created and lost, and our body can produce varying amounts of heat, unlike the near-constant heat we receive from the sun. But as far as the second law of thermodynamics goes, where we are only talking about the flow of heat, the comparison is good. The second law says nothing about how the heat is produced, only about how it flows between things.

To summarise: Heat from the sun warms the Earth, as heat from your body keeps you warm. The Earth loses heat to space, and your body loses heat to the environment. Greenhouse gases slow down the rate of heat-loss from the surface of the Earth, like a blanket that slows down the rate at which your body loses heat. The result is the same in both cases, the surface of the Earth, or of your body, gets warmer.

So global warming does not violate the second law of thermodynamics. And if someone tells you otherwise, just remember that you're a warm human being, and certainly nobody's dummy.

Principles of Planetary Climate, by R. Pierrehumbert (Cambridge Uni Press 2010). This will be available from December 2010, and goes into considerable detail of the greenhouse effect and the associated physics.

Comments

Climate_Protector - Please keep in mind that the overly simplified example I gave was a Gedankenexperiment, intended to describe the important of certain aspects of the climate system if everything else is held fixed. If the Earth were at -17C, we would have a "snowball Earth", extremely high albedo from ice sheets, and the final state would be much much colder.

That doesn't matter for the point of a GHG reducing effective emissivity. Suffice it to show that we would be hugely colder without it, and that energy levels can be higher at the surface than incoming values depending on how effectively the energy leaves.

As to the values I gave: 100% - 80% = 20% passing through without absorption. Half the 80% (40%) radiates up as well, so upward radiation is 20%+40% = 60% of 240, or 144. The difference between incoming and outgoing is 96, so this cannot be a stable state.

Given the (toy) numbers I gave, with 60% of surface going out to space, 240 / 60% * 100% = 400. That's a stable number.

Again - that was an overly simplified example to demonstrate the principle. Actual calculations are done line by line modeling 50+ layers of the atmosphere, incorporate convection and latent heat, and multiple greenhouse gases with different altitude distributions such as H2O and CO2. It's the difference between a high-school physics experiment discussing spherical frictionless objects, and a numeric integration of a complex function.

---

Opacity is a straight blockage of light, which may or may not result in some thermal radiation at possibly different wavelengths - Absorption/Emission are thermal radiation terms, directly related, and absorption/emission spectra are equal at thermal equilibrium. Opacity is the wrong physical term.

Yes, thank you! This explanation is much better (for my level of understanding at least)! A couple more questions, though:

1) Why does the atmosphere radiate 67% more IR energy to the surface as it does to space? My guess is because temperature decreases with height (at least in the troposphere), but then what's causing the temperature to drop with altitude? Is is the decrease in water vapor concentration? (because I think CO2 profile is pretty uniform throughout the troposphere, correct?). Bur water vapor amounts in the air depends on temperature. So what's driving what?

2) What is the actual enhancement of the surface temperature due to presence of GH gases, i.e. the greenhouse effect? This question relates to the comment in my previous posting about the amount of absorbed solar radiation in the absence of atmosphere and clouds.

About GHG concentrations, I just found a number about the average H2O vapor concentration in the air - 0.25%. Does this sound right? So that means that the mean concentration of all GH gases is about 0.5% or less, correct? ... It's amazing how this minute amount is able to warm the planet to such an extend!! This means the efficiency of redirecting of IR energy towards the surface by GH gases is quite high!

"As it happens, the atmosphere radiates 37.4% (199 w/m^2/532 w/m^2) of its energy to space, and 62.6% to the surface (333 w/m^2/532 w/m^2). That means it radiates 37.4% of the energy it receives by convection to space, and 37.4% of the energy it receives by evapo/transpiration to space, and 37.4% of the energy it absorbs directly from the sun to space, and 37.4% receives as IR radiation from the surface to space. It follows also that 33% (175 w/m^2/ 531 w/m^2) of back radiation comes from energy introduced to the atmosphere other than by absorbing IR radiation from the surface."

What?

How can the atmosphere radiate 199 W/m^2 to space from thermals and evaporation when it only moves 97 to the atmosphere?

What's important to realize here is that air temperature is a direct function of the internal energy of the atmosphere at any level, and IR emission is a product (result) of that temperature, not the other way around! So in the chain of cause and effects, the sequence is:

RW1 @547: "All I'm saying is an increase in CO2 concentration will increase absorption in the CO2 absorbing bands, yes, but this does not necessarily mean all of the other absorbing bands will remain constant, especially at various levels of the atmosphere where their concentrations can vary (H20 in particular). That increased CO2 will decrease total transmittance through the whole atmosphere not definite by any means - just seemingly probable."

Not only probable, but observed, as shown in this plot of the differences in brightness spectra for various wavelengths between 1970 and 1996:

So, not only is your proposition extremely improbable, it is known to be false from observation.

Also, think about what might be contributing to the internal energy of the atmosphere (particularly the lower troposphere) besides the Sun? In other words, is there another factor that can enhance the kinetic energy of air beyond the level supported by the absorbed solar solar radiation)?

RW1 @553, the total IR radiation from the atmosphere to space is 199 w/m^2. Of that, 6.4 w/m^2 will have been transported to the atmosphere by thermals, 29.2 would have been absorbed SW radiation, and 29.9 would have been carried into the atmosphere by convection.

Gentlemen, absorption and re-emission can onlyredistribute available energy, but cannot produce extra heat in the atmosphere needed to explain the near-surface thermal enhancement presently called atmospheric 'greenhouse effect'.

Did you know that convection can offset the potential warming by back radiation. If you try solving the radiative transfer simultaneously with convective heat exchange, you will see that convection can neutralize the entire effect of back radiation!

1) Your guess is correct. The vast majority of the GH effect is caused by CO2 and water vapour. As it happens, concentrations of water vapour fall to a level where IR radiation can escape to space in its most strongly absorbing frequencies at an altitude of about 5 km. For CO2, that altitude is about 8 km. That means the IR radiation escaping to space comes from a source about 30 degrees cooler than the surface for the frequencies where water vapour is a strong absorber of IR radiation, and about 42 degrees colder for frequencies where CO2 is a strong absorber (including in that part where it overlaps with H2O).

The reason the troposphere cools with altitude is because of the rate air heats (or cools) due to compression (or expansion) as it falls (or rises) in the atmosphere. Because air is cooled as it rises by expansion, and heats as it falls through compression, this establishes a stable rate of temperature change with altitude (the lapse rate) such that, if the atmosphere lies near that rate, it will not tend to rise or fall, and if it is far from that rate, it will tend to rise or fall until it is close to it. That rate is a function of the gravitational acceleration and the specific heat capacity of the gas involved.

2) The actual enhancement is greater than 33 degrees C, but the exact amount is difficult to determine, for reasons I discussed @464 on this thread.

3)The following is a graph of the H2O concentrations in the atmosphere at 100% humidity at various temperatures:

You can see that a typical concentration would be between 0.5 and 1% (approx. 33 to 66% humidity at 15 degrees C) but it can rise much higher and go much lower. You should also note that because the concentration falls sharply with falling temperature, H2O concentrations fall sharply with altitude. That is why its effective altitude for radiation to space is lower than that for CO2. It also means CO2 is relatively speaking a far more important green house gas at the poles than at the equator (where water vapour is more dominant).

Climate_Protector, you indicated that with the low concentrations involved, the GHG must have a very powerful effect. They do not have a powerful effect per molecule, but a lot of molecules are involved. As to who powerful, this is a graph of the absorption of IR by CO2 travelling through 1 meter of atmosphere at sea level at the wavelengths where it is strongest as an absorber of CO2 (courtesy of Science of Doom):

And so you can see the same thing with your own eyes:

Please ignore the comment at the end of the video about "That's exactly how CO2 works in the atmosphere ..." which, as we discussed above, presents only half of the equation.

PhysSci @561, I am not in general going to respond to your comments, which I consider to be little more than spam. If you want to discuss the issue, mount an argument, don't snipe, then hide behind an as yet unpublished paper.

However, in this case you are clearly only partially correct. Specifically, if back radiation tends to heat the surface beyond the temperature dictated by the lapse rate, convection will increase, cooling the surface. As a result, except for short term excursions (ie, over a few hours or in some cases days), back radiation is not very significant in determining average surface temperature. However, back radiation can lift surface temperatures up to the temperature determined by the lapse rate without the heat being dissipated by convection. This is an important effect in temperate zones and the poles where outgoing longwave radiation is greater than incoming short wave radiation. More importantly, this effect is very well known to atmospheric physicists and is part of the full explanation of the greenhouse effect as expounded in elementary textbooks (although it does get passed over in many popular science accounts).

"Gentlemen, absorption and re-emission can only redistribute available energy, but cannot produce extra heat in the atmosphere needed to explain the near-surface thermal enhancement presently called atmospheric 'greenhouse effect'."

PhysSci, that would be true if the climate were a static, fixed energy system. However, the climate is an open ended energy flow, not a static distribution. Energy will accumulate or dissipate based upon flow rates until input energy equals output energy. Given the limiting throughput of the atmosphere, there is more accumulated energy at the surface than the instantaneous flow rate, but that instantaneous flow rate of 240 W/m^2 enters the system and leaves it.

Sorry, Tom Curtis, another analogy. PhysSci, water flows down a river, into a dam, and out the other side. The water is much deeper at the dam than in the upstream river, pressure at the bottom of the dammed lake is much higher than at the bottom of the river, but the flow rate in and out of the dam is equal, or the level at the dam will change until that is true. Your complaint is inappropriate for this situation.

Sadly, PhysSci, it is becoming apparent to me that your grasp of the physics involved is not terribly strong. I suggest more reading on your part.

It would be very helpful if PhysSci would actually state his position and present his argument. If you are unwilling to do so until after you publish your paper then please wait til then to comment on it.

Thank you for this wonderful explanation! It gave me insight and more food for thought.

I knew that air rises when it heats up, but did not fully realize that it also cools at the same time. I did not understand that 'compression' actually heats up the falling air. From what you said: "That [lapse] rate is a function of the gravitational acceleration and the specific heat capacity of the gas involved", I figured out that gravity is somehow responsible for compressing a falling parcel of air. Could you elaborate a bit more how exactly that works?

Also, from your explanation, I gather that greenhouse gases are not determining the lapse rate. Is this right? I thought GH gases were either controlling the lapse rate or directly heating the surface, and that the lapse rate was responsible for the higher temperature on the surface. Could you provide a little more clarification on this?

This discussion has been really useful for me. I feel like I'm really advancing my understanding in a field I've been taken for granted!

"The diagram was about the flow in energy which is expressed in units of W/m^2. That is: energy (watts) over a specific area (a square meter). Are you suggesting that it should be "degrees" per square meter?"

No, I'm not. Degrees per meter i.e. distance, not area. The temperature in the tropsphere (in the diagram) should be shown as -6.5C per km (altitude). Then the author could show how it is affected by CO2, it is the second law of thermodynamics.

You also wrote:-

"Also, why are you criticizing the IPCC when the diagram you are talking about is by Trenberth, Fasullo and Kiel (2009)? "

Because the IPCC use Treberth's diagram in many of its official reports
when making the case for governmental action to reduce CO2 emissions

Trenberth has updated his diagram a number of times changing the W/m^2 numbers but never showing any temperatures or even temperature gradients. Surely if the IPPC wishes to make the case for CO2 global warming they could have chosen a diagram with temperatures on it so that the warming would be clear to all?

It a fundamental of heat transfer, W/m/K Watts per metre per degree Kelvin. You can multiply this by however many m^2 you have to determine the total power being transferred for the given temperature difference, the formula just gives the temperature gradient; in the atmosphere it is -6.5 deg. Kelvin per km.

Response: [Muoncounter] You've raised this point before. If you have an objection of substance, perhaps you can take it up directly with Dr. Trenberth and report back.

"As a result, except for short term excursions (ie, over a few hours or in some cases days), back radiation is not very significant in determining average surface temperature. However, back radiation can lift surface temperatures up to the temperature determined by the lapse rate without the heat being dissipated by convection."

I thought that back-radiation was the primary factor controlling the global surface temperature. That has been my impression all along from the popular literature describing the greenhouse effect. However, as someone has pointed out on this thread before, one cannot learn good physics from popular literature and analogies ... So, should I understand that back radiation is only marginally important for surface temperature globally because of the presence of convection? Is this another way of saying that the lapse rate is the main factor determining surface temperature?

The air heats as it falls because it is compressed by the higher pressure air around it. It cools as it rises because it expands because of the lower pressure air around it. This is an indirect effect of gravity, which is of course the reason the air becomes more dense, and under higher pressure the lower you get in the atmosphere.

GHG also impose a lapse rate on the atmosphere, however, in the troposphere, the effect of convection overwhelms that of GHG in determining the lapse rate because it takes much less time for convection to move energy than it does radiation. Radiation counter intuitively takes a long time to move energy because it only travels a short distance before being absorbed. It will then take considerable time before it is re-emitted. So, while convection carries energy quite slowly, and radiation carries it very fast (at the speed of light), convection carries it in one continuous motion, while the radiation makes a series of short journeys with very long delays in between. The tortoise and the hare come to mind.

At higher altitudes, because the molecules are greatly seperated radiation becomes the main means of carrying energy. But because the molecules a greatly seperated, very little of the Earth's radiation to space comes from those altitudes, so they can be effectively ignored.

So, in the troposphere, convection determines the lapse rate. What GHG do is determine the temperature in the upper troposphere. By determining that temperture, they also determine the temperture at the surface because the two are related by the lapse rate. And to avoid one common confusion, this is not a case of the upper troposphere warming the surface. The sun warms the surface. The lapse rate and GHG determine how efficiently the energy from the sun can escape the surface, and hence how much the surface is warmed by the sun.

Michael Sweet @571, damorbel is using the correct units, and the approximate value of the environmental lapse rate, which is critical to the greenhouse effect. (See my comments at 563 and 573.) Where he is wrong is in supposing that Trenberth's diagram from the IPCC is a model of the greenhouse effect. It is not, except in the most rudimentary terms. It is only what it claims to be, the Earth's energy budget, ie, a tabulation of what comes in and what goes out. His demand about the proper presentation of the table amounts to a demand that every diagram related to a theory should explain every feature of the theory, which is absurd.

Protector @572, back radiation is relatively unimportant in determining global temperatures, although situations arise where it is very important in determining the local temperature for a period of time. However, if back radiaton raises surface temperatures to far, this will raise temperatures at the top of the troposphere by convection. The raised upper tropospheric temperatures will result in more radiation escaping to space, thus cooling the Earth. In consequence, the temperture at the surface in the long term is set by:

1) The Lapse rate; and

2) The balance of IR radiation to space from the upper troposphere, as determined by GHG.

You need both factors. If you consider a number line representing the surface tempertures, then the lapse rate is a sloped line intersecting the number line. The point of intersection will determine the surface temperature. However, if we just know the slope, we do not know the point of intersection. We also need to know the location of at least one other point on the slope, and that is determined by the GHG in the atmosphere.

Wow, that's a whole different picture from what I had in mind. Very enlightening!...

So, it sound like the vertical pressure gradient is a key factor controlling the lapse rate at least in the troposphere, and then GH gases affect directly only the upper troposphere temperature, and controls the surface temperature indirectly through the lapse rate, correct? Let me ponder on this for a while before I continue this amazing (at least to me) discussion.

The following is a diagram to illustrate the importance of the lapse rate from one of the best simple explanations of the Green House effect that I know of. (Warning, it contains some maths; but you do not need to follow the maths to understand the explanation.)

One point the diagram illustrates which I haven't mentioned is that GHG "sets the temperature at the top of the troposphere" (which on reflection, is not the best wording) by adjusting the altitude from which the Earth effectively radiates to space at different frequencies.

You are certainly correct about radiation playing a minor role in transferring energy in the bulk of the troposphere. But I have a problem with your explanation for the 'top of the trop.' I suggest it is the absorption of ultraviolet by O2 that dominates the heating of the atmosphere above the tropopause. About 10% of the Sun's radiant energy is absorbed by O2 and of course the resultant O3. This 'stratospheric heating' occurs even with the rather small amount of UV energy because the density of air is so low 'up there'.

And, being a heating effect and causing the temperature to rise, it produces what is called, in the troposphere, a temperature inversion, a condition with warm air over cold, known to supress convection and produce stable air conditions, just the reason why jet transports like to fly in the stratosphere.

The temperature at the bottom of the stratosphere ('top of the trop.') can be -60C but it rises steadily to about 0C at 60 to 65km.

damorbel @578, you are of course correct about the stratosphere. Further, without the absorption of UV by the dissociation of O2 and O3, there would be no temperature inversion in the stratosphere. However, even without that absorption, radiation rather than convection would dominate energy transfers in the stratosphere as I have described, and for the reasons given. I had considered giving the fuller explanation, but opted for brevity.

The diagram is not about temperature. Its about incoming solar radiation expressed in W/m^2 and how it is distributed throughout the Earth's climate system, which is the proper unit of measure for that particular type of energy (Incoming Solar Radiation).

The 2009 diagram shows slightly different numbers from your example which was published in 1997 because the data has been updated. Why would Ternberth or anyone for that matter want to use 12 year old data when more up to date data is available? And again, the diagram is about the distribution of energy, not temperature.

Damorbel, "just the reason why jet transports like to fly in the stratosphere."

You should have explored this more before throwing it in the discussion as if it was fact. At mid latitudes, the average height of the troposphere is 17 km, it gets higher toward the equator, lower toward the poles. At our latitudes, transport jets fly mostly between 8 and 13 km (25 to 42000 ft pressure altitude). A number of business jets are designed to handle transonic speeds and can be comfortably flown up to 50000 ft or even higher. However, they are not true stratospheric airplanes.

Even commercial transport jets operate on a relatively thin margin of safe airspeed. As air density decreases, an aircraft needs more and more speed to generate lift, edgeing close to the speed of sound. At high altitudes, the difference between stall speed and maximum speed for the aircraft's design (beyond which flight controls may become ineffective) becomes small enough to be a concern. Stratospheric flight requires specific design or the ability to go supersonic.

Modern transport jets are not designed to fly in the stratosphere and pilots do not like to go higher than 45000 feet. Not only their safe airspeed range shrinks but the risks from a decompression accident increase dramatically. In a 2 men crew airplane, if one pilot leaves his station, the other must wearing the oxygen mask, and keep it until the other crewmember returns. At 40000 feet, you have about 18 seconds of useful consciousness if you're a healthy adult.

There is plenty of smooth air between 15 and 25000 feet, the reason why long range transport jets fly above 30000 is fuel consumption. When there is weather generating turbulence at these kind of altitudes, it is most likely convective in nature and can extend to 55000 ft or more, you can't beat it by climbing.

I'd like to get the discussion back to the topic at hand, the Greenhouse Effect, if I may (since this is so fascinating!).

I'm curious to know, if there is a broad consensus among this group about 3 aspects of the GH effect discussed above by Tom Curtis, damorbel, and myself. Since these revaluations were a real surprise to my level of understanding, I thought I'd make sure that the other expects support them as well:

1) Back radiation has a marginal influence on surface temperature due to the effect of convection;

2) Temperature lapse rate in the troposphere is controlled by convection through the vertical pressure gradient, and is not affected much by GH gases;

3) GH gases affect surface temperature only indirectly through controlling the temperature of the emission layer (where most IR radiation escapes to space) in the upper troposphere.

"the total IR radiation from the atmosphere to space is 199 w/m^2. Of that, 6.4 w/m^2 will have been transported to the atmosphere by thermals, 29.2 would have been absorbed SW radiation, and 29.9 would have been carried into the atmosphere by convection."

Let's run these numbers and see if they work:

If 40 W/m^2 passes through the atmosphere, that leaves 199 W/m^2 emitted by the atmosphere, yes. 199 W/m^2 - 36.3 W/m^2 (6.4 + 29.9) emitted out to space from thermals and evaporation = 162.7 W/m^2. That leaves an additional 162.7 W/m^2 to be emitted. If you assume 29.2 W/m^2 (37.4%) is emitted directly from the 78 W/m^2 of the energy the atmosphere absorbs from the Sun, that leaves 133.5 W/m^2 that must come from surface emitted IR. It also means 48.8 W/m^2 (out of 78 W/m^2) total is radiated down to the surface. 161 W/m^2 is absorbed directly by the surface. 396 W/m^2 - 133.5 emitted to space = 262.5 W/m^2 emitted down to the surface. 161 W/m^2 + 262.5 W/m^2 + 48.8 W/m^2 + 60.7 W/m^2 = 533 W/m^2 (396 W/m^2 required). These numbers don't work.

All units in w/m^2. Slight errors introduced by rounding, and a slight inequality exists because the Earth is accumulating energy. Other than that, it all adds up if you make sure to use the correct figures.

I think it was Tom Curtis, who made a comment earlier that it's difficult and probably physically not sound to try separating IR fluxes like that, because we are dealing here with absorption/re-emission NOT reflection of radiation. From what I've read elsewhere, these two processes are physically quite different ... But maybe the other experts would not agree.

"And again, the diagram is about the distribution of energy, not temperature. "

Rick in what form can one quantify the "loose" atmospheric energy? As you say, it is not temperature, so how do you know is there...can it be measured? Measured of course, not based on temperature. And by what means is the atmospheric energy stored?

Protector @582, I could have stated (3) better, but it should do for current discussion. More accurately, the GHG concentration determines the altitude of the effective radiation. The need to balance incoming solar radiation with outgoing longwave radiation then determines the temperature at that altitude, which then governs the temperature at the surface by means of the lapse rate.

DB, thanks, but I do not have entire confidence in myself. I try though.

RW1 @586, until you can identify a physical mechanism whereby CO2 or H2O molecules in the atmosphere can determine the original source of the energy they are emitting, your claim is clearly wrong. Bear in mind that the emitting molecule may not have been the molecule that originally absorbed the energy, but may have gained it after a series of collisional transfers in the atmosphere.

There is 239 W/m^2 of post albedo coming in, 239 leaving at the top of the atmosphere, and 396 W/m^2 at the surface. Your energy flow calculations do not adhere to this; thus, Conservation of Energy is not being met.

You don't seem to understand this, so I'll break it down into a series of separate questions and we'll go from there:

1. Do you agree that 239 W/m^2 of post albedo enters the system and ultimately becomes 396 W/m^2 at the surface?

2. Do you agree that the atmosphere cannot create any energy of its own?

3. Do you agree that 239 W/m^2 is leaving the system at the top of the atmosphere and all of this is radiative?

4. Do you agree that all of the 396 W/m^2 emitted by the surface is radiative?

5. Do you agree that the 396 W/m^2 emitted by the surface is a result of its temperature and nothing else?

6. Do you agree that latent heat and thermals are kinetic energy (non radiative) moved into the atmosphere from the surface?

4. Do you agree that because latent heat and thermals are kinetic, their energy moved into the atmosphere is in addition to or independent of surface emitted radiation?

"RW1 @586, until you can identify a physical mechanism whereby CO2 or H2O molecules in the atmosphere can determine the original source of the energy they are emitting, your claim is clearly wrong. Bear in mind that the emitting molecule may not have been the molecule that originally absorbed the energy, but may have gained it after a series of collisional transfers in the atmosphere."

I'm not claiming trade offs do not occur between radiative and kinetic energy in the atmosphere - they clearly do, multiple times over I'm sure. The point is the net effect of all the trade offs have to be zero, because all the energy leaving at the top of the atmosphere is radiative and all the energy emitted by the surface is radiative.

RW1 @592: Questions 2, 3, 4, 6 and 7 are all answered "yes". For Question 1 and 5, the answer is "No".

1) The energy absorbed at the surface is the Incoming Solar Radiation absorbed at the Surface (approx 161 w/m^2) plus the Back Radiation absorbed at the surface (approx 333 w/m^2). If you do not include both terms, the result will inevitably show an inequality of energy flows! The energy leaving the surface is the surface radiation plus the convective flux plus the evapo/transpiration flux. Again, if you don't include all three terms, you will inevitably arrive at an inequality. Saying that 239 w/m^2 becomes 396 w/m^2 is to directly assert the non-conservation of energy.

Note, your claim that my caclulations do not include the incoming non-reflected solar radiation, the out going longwave radiation, and the surface radiation is simply false. All are included at their appropriate places, as can be easily checked.

5) The surface radiation is a function of temperature and emissivity, which is not 1 at any location, though very close to 1 at most.

@594: The incoming and outgoing energies are both radiative. All of the energy comes from the sun, but some of it is shuffled back and forth a bit before it leaves the system. (Total energy from other sources is, I believe, significantly less than 1% of the total, and can be ignored for practical purposes.)

RW1:
Please continue this discussion. You are doing an excellent job.
One thing to remember in the conservation of energy is that each time a collission occurs, there is a net loss of energy to gravity. This also expends heat energy.

RW1 @595, all energy "emitted" from the surface is radiative only because we do not talk about "emitting" convection, or evapo/transpiration. Not all energy flux from the surface, however, is radiative. In fact, only 80% of it is. And some of the energy flux carried by convection and evapo/transpiration makes its way to space. Do you deny that?